Project Summary: Many cardiovascular (CV) clinical trials feature complex composite outcomes consisting of multiple types of (possibly recurrent) events, e.g., heart failure, myocardial infarction, stroke, and death. In addition, due to the chronic nature of the disease, these long-term trials often suffer from non-randomized cohorts as a result of informative dropout, a complication that shakes the foundation of randomized controlled trials as the gold standard for clinical inquiry. Motivated by the INVESTED trial, an ongoing multi-season CV trial comparing two dosages of influenza vaccine (for which we serve as lead statisticians), this proposal aims to develop novel statistical methodology that is more robust, more efficient, and better suited for such long-term CV trials. This goal will be achieved via three specific aims. For specific aim 1, we tackle the problem of non-randomized cohort adjustment under a comprehensive framework of time-to-event analysis, including the well-known Kaplan-Meier curve, log-rank test, Cox regression model, and other methods for recurrent events and competing risks. We will develop a robust inverse probability of treatment weighting (IPTW) approach with non- /semi-parametrically estimated weights to correct for selection bias in non-randomized cohorts. For specific aim 2, we generalize the newly developed win-loss approach for composite outcomes from two-sample testing to the regression setting. The win-loss approach is targeted for composite endpoints consisting of prioritized components, e.g., death over non-fatal events. The information it extracts from multiple prioritized time-to- event outcomes is fuller, more interpretable, and clinically more relevant than that contained in time to the first event, the traditional target of analysis. For specific aim 3, we further generalize the win-loss approach to a nonparametric framework that allows the win-loss probabilities to depend on the follow-up time. Both generalizations of the win-loss approach will proceed in an estimand-driven way as recommended by the recently published ICH-E9(R1) Addendum. Statistical efficiency of the proposed procedures will be studied thoroughly using modern semiparametric and weak convergence theories. Development of efficient procedures will help minimize trial costs. User-friendly R packages that implement the algorithms of the proposed methods will be developed and disseminated through https://cran.r-project.org.